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4024/21 Oct/Nov 2022, Question 9: Solving Linear Equations

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Form and solve an equation in n from Kate's operations on a number, then simplify a division of two algebraic fractions into one fraction.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Write an equation in n for subtracting 8, multiplying by 3, giving 11 less than n, then solve for Kate's number.

  1. 13(n − 8) = n − 11
  2. 23n − 24 = n − 11
  3. 33n − n = −11 + 24, so 2n = 13
  4. 4n = 6.5

Answer6.5

Part (b) · 3 marks

Divide (x² − 4)/2 by (x² + 2x)/4 and express the result as a single simplified fraction.

  1. 1x² − 4 = (x + 2)(x − 2) and x² + 2x = x(x + 2)
  2. 2(x + 2)(x − 2)/2 × 4/(x(x + 2))
  3. 3= 4(x − 2)/(2x)
  4. 4= (2(x − 2))/x

Answer(2(x − 2))/x or (2x − 4)/x or 2 − 4/x

Stuck on a step? Read the free lesson: Solving Linear Equations

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 9.
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